For rasterizing in fire studies is convenient that you first get polygon for layer extent that contain all years.
In my case, I considered three years (1990-1992) for Portugal case. That polygon at next image:
it has this extent:
xMin,yMin 82175,9600 : xMax,yMax 356140.00,572100.00
-te 82175 9600 356140.00 572100.00
as parameter syntax of gdal_rasterize command.
Assuming the same raster resolution (-tr 30 30), my three gdal_rasterize commands are:
gdal_rasterize -burn 1 -te 82175 9600 356140.00 572100.00 -tr 30 30 fire_1990.shp fireRaster1990.tif
gdal_rasterize -burn 1 -te 82175 9600 356140.00 572100.00 -tr 30 30 fire_1991.shp fireRaster1991.tif
gdal_rasterize -burn 1 -te 82175 9600 356140.00 572100.00 -tr 30 30 fire_1992.shp fireRaster1992.tif
After running each one at the bash console, I loaded all resulting raster at Map View of QGIS. In the case of 1990 year, it can be observed (pseudocolor with two classes, Spectral ramp):
If I hide fire_1990 shapefile, I got a similar behavior as in your case: small areas look as not rasterized but they were.
Zoom an arbitrary zone where this behavior occurs, it permit to corroborate that they really exist.
I think that in your case could be an extent issue.